CT systems for generating quantitative tomographic phase-contrast images with the aid of at least one phase grating in the beam path of the emitter-detector system, that is to say using interferometric measurement methods, are generally known. It is very demanding to produce the X-ray optical gratings required for this because they have to have structure geometries with a structure width of approximately 1 μm and a structure height of approximately 100 μm, corresponding to an aspect ratio of approximately 100. The use of said method in CT systems that can be used clinically is made more difficult as a result of this problem, which is difficult to solve technologically on a clinical scale.